Schottky anomaly in a repulsive lattice polymer

We examine the specific heat of a self-avoiding polymer on a square lattice with repulsive interactions, which exhibits the Schottky anomaly, a peak in the low-temperature region without a divergence in the thermodynamic limit. The low-temperature tail of the specific heat can be explained by the bending energy imposed due to repulsive next-nearest-neighbor interactions, which play the role of local interactions along the chain. For comparison, the specific heat of a polymer without nonlocal self-exclusion is also considered, wherein only the bending energy is present, which is analytically solvable. The specific heat of the self-avoiding repulsive next-nearest-neighbor polymer is also shown to be robust with respect to the addition of repulsive nearest-neighbor interactions, which act only as nonlocal perturbations causing a slight change in the specific heat in the high-temperature region. We also discuss the relevance of the lattice effect in the context of real polymers.